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Math Help - Find Domain

  1. #1
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    Solve equations

    Can anyone please help me in equation form with the answers to the following questions?

    1. Give the range of the function y = tan^-1 x

    2. Give the value of tan^-1 5
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  2. #2
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    Quote Originally Posted by Kiwigirl
    Can anyone please help me in equation form with the answers to the following questions?

    1. Give the range of the function y = tan^-1 x
    There are two ways to do this problem. One way is the cowardly way they teach in school using a graph in that case look below to see that the range is,
    y\in (-\pi/2,\pi/2)

    The second way. The function \tan^{-1}(x) is defined as the inverse function of the function,
    \tan x \mbox{ on } -\pi/2<x<\pi/2. Now there is a rule that the range of the inverse function is the domain of the orignal function. Since the domain of the original function is (-\pi/2,\pi/2) thus the range of \tan^{-1}(x) is (-\pi/2,\pi/2)

    There is actually a third way (much more advanced). Find all such y such as the equation y=\tan^{-1}(x) has a solution.
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